Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$
Answer
$${{6 - \pi \sqrt 3 } \over {12}}$$
2
IIT-JEE 1983
Subjective
Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and
the ordinates at $$x=2$$ and $$x=4$$. If the ordinate at $$x=a$$ divides the area into two equal parts, find $$a$$.
For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
Answer
Solve it.
Questions Asked from Definite Integrals and Applications of Integrals
On those following papers in Subjective
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